A circle with circumference $18\pi$ has an arc with a $310^\circ$ central angle. What is the length of the arc? ${18\pi}$ ${310^\circ}$ $\color{#DF0030}{\dfrac{31}{2}\pi}$
Solution: The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360^\circ} = \dfrac{s}{c}$ $\dfrac{310^\circ}{360^\circ} = \dfrac{s}{18\pi}$ $\dfrac{31}{36} = \dfrac{s}{18\pi}$ $\dfrac{31}{36} \times 18\pi = s$ $\dfrac{31}{2}\pi = s$